Course Unit Page

Teacher Cesare Zanasi

Learning modules Mirko Maraldi (Modulo Mod 1)
Cesare Zanasi (Modulo Mod 2)
Giovanni Molari (Modulo Mod 3)

Credits 10

SSD MAT/06

Teaching Mode Traditional lectures (Modulo Mod 1)
Traditional lectures (Modulo Mod 2)
Traditional lectures (Modulo Mod 3)

Language Italian

Teaching Material

Course Timetable from Sep 18, 2018 to Dec 18, 2018
Course Timetable from Sep 24, 2018 to Dec 10, 2018
Course Timetable from Sep 19, 2018 to Dec 19, 2018
Academic Year 2018/2019
Learning outcomes
Mathematics: The students will be able to operate with real numbers, to understand the algebraic calculation and the basic properties of the geometrical figures. The student will be able in general to: use the mathematical knowledge and the mathematical tools; to set and solve problems; to learn new concepts on the base of its experience and the previous knowledge. In Statistics the student will learn the main methods and tools for the qualitative and quantitative inferential and descriptive analysis. In particular: interpret and critically evaluate the statistical information; produce and process raw data; apply the statistical approach to the natual and social sciences topics related to animal production.
In Physics: the student will learn the meaning of the different units of measure; the meaning of the basic physics terms; the basic principls of physics; the student will then be able to follow the successive courses of physiology, food technology, animal production related buildings and machinery.
Course contents
Module 1 Mathematics
An attempt will be made to answer, collectively, the following questions: what is Mathematics? Can Mathematics teach us anything valuable? During the process of finding an answer to these questions, we will try to overcome the common point of view under which Mathematics is only a matter of solving exercises and doing calculations. During the course:
 we will highlight the concise character of the mathematical notation (each graphic sign is necessary, no signs are redundant)
 we will examine in greater depth some of the topics already studied in the previous highschool classes and we will introduce some new upperlevel topics
 we will observe how the apparent complexity and rigour in the definition of a certain object is necessary to extend its field of existence and applicability
In detail, the topics covered will be:
PREPARATORY TOPICS:
 scientific books/papers: how to use and how to cite them
 basic mathematical notation; order of operations
 proportions
 linear and secondorder algebraic equations and their solution
 polynomials
 the Cartesian plane and how to draw it
 area and volume of simple plane figures and simple solids
 binary operators and properties of binary operations: associative and commutative properties; neutral, null and opposite elements; examples
 unary operators: linear operators; definition of linearity; examples
TRIGONOMETRY
 similar triangles; definition of sine, cosine, tangent
 the unit circle and fundamental theorems of Trigonometry
 sine, cosine and tangent values for special angles
 the importance of the cosine in the projection of vectors and of the sine in the evaluation of the area
REALVALUED FUNCTIONS OF REAL VARIABLES
 intervals: open, closed, bounded, unbounded
 Cartesian product of intervals
 definition of a function and examples of functions and nonfunctions; domain, codomain, image
 injective, surjective and bijective functions; the inverse function and functions composition
 drawing functions on the Cartesian plane
 odd and even functions; examples
INTEGRALS – I
 integral as the signed area of a function graph: rectangle algorithm
 integrals properties: domain decomposition; limits swap; integrals of odd and even functions
LINEAR ALGEBRA
 vectors as R^{n} objects; matrices as tabular lists of vectors
 operations with matrices: sum, multiplication, scalar multiplication
 matrices representative of linear transformations; proof of linearity
 special transformations: scaling; mirroring; identity matrix; null matrix; inverse matrix;
LINEAR FUNCTIONS
 equation of a straight line: explicit, implicit and parametric forms
 straight lines as linear functions and affine functions; proof of linearity, surjectivity, injectivity; proof of evenness and oddness
 directional cosines
 equations of a straight line and of a plane in R^{3}
NONLINEAR FUNCTIONS
 the exponential function; properties of exponents
 the logarithmic function; properties of logarithms; logarithmic and semilogarithmic scales
 periodic functions and trigonometric functions: sine, arcsine; cosine, arccosine; tangent, arctangent
LIMITS OF FUNCTIONS
 rigorous definition of the limit of a function; using the definition to determine the limit of simple functions; on continuous functions
 definition of limit at infinity; limit at infinity of simple functions; asymptotic behaviour of polynomials
 nonexistence of the limit; sin(x) at infinity; 1/x at zero
 behaviour of polynomials at zero; definition of the term “asymptotic”
 special limits: (sin x)/x for x à 0; (1cos x)/x for x à0; (1cos x)/(1/2 x^2) for x à0
 comparison of the endbehaviour of the functions x, ln(x), exp(x), x^{N}
DERIVATIVES
 equation of the secant to a curve; difference quotient; limit of the difference quotient; rigorous definition of a derivative
 tangent equation; linearization of a curve; physical meaning of a derivative
 maximum and minimum values of a function and link with the first derivative of the function; Fermat’s theorem and applicability range
 differential operators and proof of linearity
INTEGRALS – II
 the integral operator as the inverse of the differential operator
 the fundamental theorems of calculus
 proof of linearity of the integral operator
 physical meaning of the integral
 mean of a function
Module 2 Statistics
Theory
Introduction: Definition and goal of statistics. Structure of Statistics. Definition of Universe, collective, population, sample. Classification.
Classification schemes: omograde and eterograde classes, numerosity,intensity and frequence. Graphical representations in statistics.
Measures of central tendency: Arithmetic and geometric mean, central value, median and mode.
Measures of statistical dispersion: standard deviation, variance, coefficient of variation.
Probability: Definiiton and assioms of probaility.Binomial and normal distribution.Standardized normal distribution. Theory of errors.
Sampling: general features and meaning.
Statistical inference: sample sum and mean, interval of confidence, Hypothesis test. chisquare test.Covariance correlation and linear regression.analysis of Variance.
Group work:application of descriptive and inferential statistical techniques to simple cases related to the animal production sector
Readings/Bibliography
Module 1 (Mathematics)
 Teacher’s notes
 Internet
 Textbooks and other material provided during the class
D. Benedetto, M. Degli Esposti, C. Maffei, Matematica per le scienze della vita, Casa Editrice Ambrosiana.
Module 2 (Statistics)
Teacher notes and slides
Internet + other material provided during the class
Module 3 (Physics)
Fondamenti di Fisica. Halliday D., Resnick R., Walker J. Casa editrice ambrosiana
Elementi di Fisica. Ageno M. Bollati Boringhieri
Teaching methods
Classroom lessons and group works on case studies
Assessment methods
The final mark of the integrated course will be calculated as an arithmetic mean of the three different modules.
In particular: the modules Mathematics involves a first preliminary written test; if the test is passed an oral examination will follow.
The module Staitstics will involve a written test with both multiple choice quesitons and open quesitons.
Ther module Physics involves and oral examination lasting about 30 mins
The marks in each module will be valid for 3 years. That is after the first module exam results the student will have three years to finalize the exams for the remaining two modules of the integrated course
Teaching tools
Mathematics: papers and slides
Statistics: online and offline statistical software, slides and papers
Phyisics: papers and slidesOffice hours
See the website of Cesare Zanasi
See the website of Mirko Maraldi
See the website of Giovanni Molari